2,367 research outputs found
Convergence Theorems for Hierarchical Fixed Point Problems and Variational Inequalities
This paper deals with a modifed iterative projection method for approximating
a solution of hierarchical fixed point problems for nearly nonexpansive
mappings. Some strong convergence theorems for the proposed method are
presented under certain approximate assumptions of mappings and parameters. As
a special case, this projection method solves some quadratic minimization
problem. It should be noted that the proposed method can be regarded as a
generalized version of Wang et.al. [15], Ceng et. al. [14], Sahu [4] and many
other authors.Comment: 12 pages. arXiv admin note: substantial text overlap with
arXiv:1403.321
The Forward-Backward-Forward Method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces
Tseng's forward-backward-forward algorithm is a valuable alternative for
Korpelevich's extragradient method when solving variational inequalities over a
convex and closed set governed by monotone and Lipschitz continuous operators,
as it requires in every step only one projection operation. However, it is
well-known that Korpelevich's method converges and can therefore be used also
for solving variational inequalities governed by pseudo-monotone and Lipschitz
continuous operators. In this paper, we first associate to a pseudo-monotone
variational inequality a forward-backward-forward dynamical system and carry
out an asymptotic analysis for the generated trajectories. The explicit time
discretization of this system results into Tseng's forward-backward-forward
algorithm with relaxation parameters, which we prove to converge also when it
is applied to pseudo-monotone variational inequalities. In addition, we show
that linear convergence is guaranteed under strong pseudo-monotonicity.
Numerical experiments are carried out for pseudo-monotone variational
inequalities over polyhedral sets and fractional programming problems
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